Answer: D) (x+1)(x + 2)(x-3)
This is because the roots are x = -1, x = -2 and x = 3
Simply get all the numbers to each side to have 0 on the right side
x = -1 turns into x+1 = 0
x = -2 turns into x+2 = 0
x = 3 turns into x-3 = 0
The three factors are (x+1), (x+2) and (x-3)
Which leads to (x+1)(x+2)(x-3)
The correct answer is 1/8.
1) To make a rectangular box you need to cut squares from the four corners of the rectangular sheet.
2) Call x the length of the sides of the squares cut off.
3) The base of the box will have dimensions: (13 - 2x) and (8 - 2x)
4) The height of the box will be x
5) The volume of the box will be the area of the base times the height:
Volume = (13 - 2x)(8 -2x)x = (4x^2 - 42x + 104)x = 4x^3 - 42x^2 + 104x
6) The maximum volume is calculated by finding the point where the derivative of the volume is zero =>
d (volume) / dx = 12x^2 - 84x + 104 = 0
7) Solve the quadratic equation 12x^2 - 84x + 104 = 0
=> 4(3x^2 - 21x + 26) = 0
=> 3x^2 - 21x + 26 = 0
=> 3 (x^2 - 7x) + 26 = 0
=> 3 [(x - 7/2)^2 - (7/2)^2] + 26 = 0
=> 3 (x - 7/2)^2 - 3* 49/4 + 26 = 0
=> 3 (x - 7/2)^2 = 3*49/4 - 26
=> (x -7/2)^2 = (49/4 - 26/3)
=> x = 7/2 +/- √(49/4 - 26/3)
x = 7/2 + √3.583 and x = 7/2 - √3.583
x = 5.393 and x = 1.607
=> Volume =
1) 4(5.393)^3 - 42(5.393)^2 + 104(5.393) = -33.26 ---> it does not have physical meaning
2) 4(1.607)^3 - 42(1.607)^2 + 104(1.607) = 75.27 ---> this is the answer
Answer: 75.27 in^3
Answer: 225g
Step-by-step explanation:
Total mass (g) of solids - Total mass (g) of liquids
385g-160g.
We add up the SOLIDS: steel block, glass block, marbles, and nails to get 385g, and the LIQUIDS: Orange juice and Vinegar to get 160g. Subtract the two to get 225g.
Answer:
less than or equal to it hope this helps you!
